The important thing here is the prayer of faith and not so much the oil. It is done in the name of the Lord to remind us that the healing comes from God. All people die; James cannot mean that in every instance every sick person is healed. Faith is confidence in God's power. He can heal with or without medical treatment, against the background of His will. When our prayer goes unanswered it is not because of our lack of faith but because God did not grant it.